Question

the volume of a right circular cone is 1232 cm³. if the radius of its base is 14 cm find its curved surface.

Answer 1

1232÷ 14= 88 is answer its curved surface area

Answer 2

The curved surface area is $88\sqrt{58}$ cm².

Step-by-step explanation:

It is given that,

Volume of cone = 1232 cm³

Radius of its base = 14 cm

Volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

where, r is radius and h is height.

Substitute V=1232, r=14, $\pi=\frac{22}{7}$ in the above formula.

$1232=\dfrac{1}{3}\cdot \dfrac{22}{7}\cdot (14)^2\cdot h$

$1232=\dfrac{616}{3}h$

Multiply both sides by  $\frac{3}{616}$.

$1232\times \dfrac{3}{616}=\dfrac{616}{3}h\times \dfrac{3}{616}$

$6=h$

The height of the cone is 6 cm.

Curved surface area of cone is

$A=\pi r\sqrt{r^2+h^2}$

Substitute r=14, h=6 and $\pi=\frac{22}{7}$ in the above formula.

$A=\dfrac{22}{7}(14)\sqrt{14^2+6^2}$

$A=44\sqrt{232}$

$A=88\sqrt{58}$

Therefore, the curved surface area is $88\sqrt{58}$ cm².

#Learn more

Find the volume,curved surface area and the total surface area of a cone having base radius 35cm and height 84cm.

https://brainly.in/question/2607965